Non-Gibbsian limit for large-block majority-spin transformations |
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Authors: | Dorlas T C van Enter A C D |
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Institution: | (1) Dublin Institute for Advanced Studies, Dublin 4, Ireland;(2) Lady Davis Fellow, Department of Physics, Technion, 32000 Haifa, Israel;(3) Present address: Department of Mathematics, University of Texas at Austin, 78712 Austin, Texas |
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Abstract: | We generalize a result of Lebowitz and Maes, that projections of massless Gaussian measures onto Ising spin configurations are non-Gibbs measures. This result provides the first evidence for the existence of singularities in majority-spin transformations of critical models. Indeed, under the assumption of the folk theorem that an average-block-spin transformation applied to a critical Ising model in 5 or more dimensions converges to a Gaussian fixed point, we show that the limit of a sequence of majority-spin transformations with increasing block size applied to a critical Ising model is a measure that is not of Gibbsian type. |
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Keywords: | Non-Gibbs measure real-space renormalization |
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